WineGuyD,
Since this is only your third shave, you're doing great. Your razor is as sharp as it can be so your focus needs to be on beard prep and shaving technique.
You've already received some great advice concerning beard prep. Consider also the use of hair conditioner, as it makes a huge difference for me. After you get out of the shower, apply some hair conditioner to your beard and rub it in well. Leave it on your face for a few minutes while you build your lather. After you're done building your lather, rinse the conditioner off your face before lathering up. You should find your beard is noticeably softer than your regular prep. If it doesn't feel softer, try using more conditioner and leaving it on your face a few minutes longer. (Changing your ritual to making über lather would accomplish that.)
Consider the use of a pre-shave oil or Proraso pre/post shave before applying your lather. Proraso pre/post shave has made as big an improvement in my beard prep as the use of hair conditioner. An aside: I started substituting Noxema cleansing cream for Proraso pre/post shave and I think I like it better. It does not have as strong a menthol fragrance as the Proraso, but it does as good a job for beard prep, is cheaper to purchase and is available in most drugstores and supermarkets.
My first few shaves felt quite similar to the experience you describe. As for improving your technique, reduce the angle of your blade each time you feel it pulling. In other words, if you wanted to slice your face open with your straight razor, you would hold it at a 90º angle (perpendicular) to your skin. Laying the side of your razor flat against your skin places it at a 0º angle. So whenever your feel your razor start to pull, move it closer toward a 0º angle until it stops pulling. This is especially important when shaving your chin.
Don't forget to stretch your skin! The angles of your chin will be especially challenging because you need to change the angle of the razor through even the shortest of strokes. Be creative in trying different ways to stretch your skin and you'll find your technique improving.
Lastly, trust your right brain. During each shave you get under your belt, think about the challenges the various parts of your face and beard present you with. Your right brain will come up with solutions to these problems and will lead your hands into new strokes and techniques for your face if you allow it. How? Just keep telling yourself "This is something I can do." And BELIEVE it!
Namaste,
Morty -_-